An adaptive local discontinuous Galerkin method for nonlinear two-point boundary-value problems (Q2189411)

This paper analyses a local continuous Galerkin method for nonlinear two-point boundary value problems. Radau quadrature methods of degree \(p\) are used to construct residual-based a posteriori error estimates of order \(p+1/2\) under appropriate smoothness conditions on the solution. These local and global error estimates allow an adaptive mesh refinement. Numerical results illustrate the theory.